Find the total area of the region between the x-axis and the graph. y= 2x - 6x? + 4x, Osxs2 Total area = |(Simplify your answer.)

Q: Find the area of the shaded region. y y=9x-x² 20 15 7, 14) 10 y= 2 x 2 4 6. 8 10

A:

Q: Find the total area of the region between the x-axis and the graph of y = - x´ - 3x, - 4 <x54.

A: Given query is to find the attached area of the region.

Q: Find the area of the region enclosed by y = 4 / x, y = 4x and x=2

A:

Q: Find the area of the shaded region. y y = x - 15 x 20 10 y= x (4, 4) -6 2 (-4, -4) - 10 - 20 A =

A:

Q: Find the area of the region belowy = x3x+5 and above y = 3 for 3 < x <6. Area =

A: Proceed as shown below

Q: Find the area of the region inside the circle r = 5V2 and above the line r = 5 csc 0.

A:

Q: Find the area of the region below y=x^2−x+2 and above y=2 for 3≤x≤6.

A: The given curves are y=x2−x+2 and y=2 and the interval is 3≤x≤6 To find the area of the region.

Q: Determine the area below y = 3 + 2x - x² and above the x-axis

A:

Q: Find the shaded area enclosed by y = 8x² and y = x* – 8x² within –4<x<4. y- &r y-x* - 8r

A: Consider the region bounded by the curves y=8x2 and y=x4-8x2 within the interval -4≤x≤4. Observe…

Q: Find the total area of the shaded regions. y=2-x -2

A: Provided figure is: The total area is divided into 3 regions A1, A2 and A3.

Q: find the total area between the region and thex-axis. y = x3 - 3x2 + 2x, 0 ≤ x ≤ 2

A: Given function or curve,  y = x3 - 3x2 + 2x,        0 ≤ x ≤ 2 To find total area between the curve…

Q: Determine which graph corresponds to the area enclosed by the curves y 3x and y = x2 + 7.

A:

Q: Find the total area between the region and the x- axis. y = x3 – 3x? + 2x -1 sxs2

A: Consider the curves, y=x3-3x2+2x  ;       -1≤x≤2

Q: Find the area of the region below y = x² + x – 2 and above y = 6 for 3 < x < 6.

A:

Q: X = -y A y 2Fx = 2- y² -2

A: Recall: Formula Area=∫abf(y)-g(y)dy  We have,  f(y)=2-y2, g(y)=-y

Q: Find the total area of the shaded region. Ay 10 Q 6- y = 5 y=x y= 2- 20 10

A:

Q: Find the total area between y = 25 - x² and the x-axis for 0 < x≤ 6. Area

A: Given is the curve y=25-x2. The objective is to find the total area between this curve and x axis.…

Q: Find the exact area of the region that lies beneath the curve y 4x-4, 1 < x < 6.

A: The exact area under the region of the curve is=∫164x-4dxWe know that…

Q: Find the area of the region below y = x² + 2x 4 and above y = 3 for 2 < x < 5. %3D Area

A: Recall:            Area=  ∫abf(x)-g(x)dx  We have, f(x)=x2+2x-4, g(x)=3, a=2, b=5

Q: Find the area of shaded region.

A: Consider the graph,

Q: Find the area of the region below y = x² – 2x + 5 and above y 3 for 2 < a < 5.

A: To find area under the curve Shown below in shaded part

Q: Find the area of the region below y = x² + x – 4 and above y = 6 for 3 < x < 6.

A: • First, we need to sketch the given parabola and identify the region whose area is to be found.…

Q: Find the area of the shaded region. y y=5x-x (3, 6) 4 2 y=2 x 1 2 3 4

A:

Q: Find the area of the shaded region. y=x-4 y= /2x 2. 8. 10 x -4 2.

A: Given query is to find the area of tha shaded region.

Q: Find the area of the shaded region below. у y =Vx 2 x=2 1 y=- x1 Area

A:

Q: Find the area of the shaded region. 15) y=-x4 y = x2 - 2x C) 2 76 D)- 15

A: From the given graph. Use the double integration method to calculate the bounded…

Q: Find the total area of the region between the x-axis and the graph of y=-x-3x, -4sxs3.

A:

Q: Find the total area of the region between the x-axis and the graph of y = - x- 3x, - 5<x<4.

A:

Q: Find the total area of the region between the x-axis and the graph. y = 2x° – 6x + 4x, 0sxs2 3 2

A:

Q: Find the area of the region enclosed by the graphs of y = x2    and y = 6x – 2x2

A:

Q: Find the area of the shaded region. y 15 y = 7x-x² 10 (5, 10) 5 y= 2 x 4 6. Enhanced Feedhaclo

A: We can application integration in order to solve the given problem.

Q: Find the area of the shaded region. x = -y x = 2 – y? -2 2 10 В

A:

Q: Find the area of the region below y=x2−x+2 and above y=3 for 2≤x≤6. Area =

A: The objective is to find the area of the region.

Q: Find the area of the region below y = x2 – 4x + 12 and above y = 4 for 2 < x < 5. Area =

A:

Q: Find the area of the shaded region. x = -y 2 x = 2 - -2 A B 10 3 2.

A: Given query is to find the area of the shaded region.

Q: Find the area of the region between y = 6x² and y = x² + 7.

A:

Q: Graph the equations and shade the area of the region between the curves. y = x2 and y = -x² + 24x

A: topic  - area between curves

Q: Find the area of the region, enclosed by the cureK = 4 – x', -2<x<2

A: The area(A) bounded by the cartesian curve y=f(x) and the x-axis between the limits x=a and x=b…

Q: Find the area of the shaded region. square units y = x3 y = x + 6 8. -6 -5 -4 -3 -2 4 -IN

A:

Q: find the total area between the region and thex-axis. y = -x2 - 2x, -3 ≤ x ≤ 2

A: The region and the x-axis given is y = -x2 - 2x, -3 ≤ x ≤ 2. To find the area  between the region…

Q: Find the total area of the shaded regions y = x y = -x² + 2x y = x3 .5 -05 0,5 15

A:

Q: Find the area of the shaded region. X = y 6 x = 27 / y2 6.

A: Area between the curve x=f(y) and x=g(y) on [a, b] is, A=∫abfy-gydy

Q: Find the area of the region. y = 81 – x4 y 80 60 40 - 4 -2 2 4 20

A: From the graph calculate the region for the integration.

Q: Find the area of the shaded region. y = x² + 1 ... 5 y = x -1 2.

A: In given problem we find the area by using the Definite Integration .

Q: Find the area of the shaded region. f(x) = x – 8x° + 21x, g(x) = 20x + 50 3

A: Intersection…

Q: Find the area of the region. y = 81 – x4 y 60 40 20 -4 -2 2 4

A: Given query is to find the area enclosed by the curve : y = 81-x4

Q: Find the area of the shaded region. y x = y - 4 y 15 5 4'2 2 -6 -5 -4 3 -2 X= y-y -2 -4 -6F

A: Given, The right function   x = y -y2  and left function     x = y2 - 4y Point of intersection of…

Q: Find the total area of the region between the curve and the x-axis. y = 2x +7;1sxs5 52 26 9. O 18

A:

Q: 8. y = 3x² – 3, -2< xs 2

A:

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.